plotting contours on a sphere

• To: mathgroup at smc.vnet.net
• Subject: [mg119473] plotting contours on a sphere
• From: J Davis <texasautiger at gmail.com>
• Date: Sun, 5 Jun 2011 07:04:18 -0400 (EDT)

```I would like to plot the contours of a given function f on the surface
of a sphere.

More specifically, I'd like to "wrap" the contours in p2 below onto
the surface of the sphere in p3.

f[\[Theta]_, \[Phi]_] = Sin[\[Theta] + \[Phi]];
p1 = Plot3D[f[\[Theta], \[Phi]], {\[Theta], 0, 2 Pi}, {\[Phi], 0, Pi},
PlotRange -> All, AxesLabel -> {\[Theta], \[Phi]},
ColorFunction -> ColorData["TemperatureMap"]];
p2 = ContourPlot[
f[\[Theta], \[Phi]], {\[Theta], 0, 2 Pi}, {\[Phi], 0, Pi},
PlotRange -> All, FrameLabel -> {\[Theta], \[Phi]},
ColorFunction -> ColorData["TemperatureMap"]];
p3 = SphericalPlot3D[1, {\[Phi], 0, Pi}, {\[Theta], 0, 2 Pi},
ColorFunctionScaling -> False,
ColorFunction ->
Function[{x, y, z, \[Theta], \[Phi], r},
ColorData["TemperatureMap"][
Rescale[f[\[Phi], \[Theta]], {-1, 1}]]]];
GraphicsRow[{p1, p2, p3}, ImageSize -> 750]

Thanks in advance for any insight you can offer.

Best,
John

```

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